Estimation of the parameters of a random amplitude sinusoid by correlation fitting

We consider the best asymptotic accuracy that can be achieved when estimating the parameters of a random-amplitude sinusoid from its sample covariances. An estimator based on matching in a weighted least-squares sense the sample correlation sequence to the theoretical sequence is presented. The asymptotic properties of the estimator are analyzed. A lower bound on the estimation of the parameters from sample covariances is derived. This bound is shown to be attainable by appropriately choosing the weighting matrix. However, the unweighted nonlinear least-squares estimate performance is shown to come close to the lower bound. The influence of the number of samples, the number of correlation samples, and the lowpass envelope characteristics are studied. Finally, a comparison with Yule-Walker (YW) methods is given.